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Mathematics

Grade5

Easy

Question

Add $9 over 22 space and space 5 over 11$ .

$\frac{14}{33}$
$\frac{19}{22}$
$\frac{8}{21}$
$\frac{6}{11}$

hint Hint:

In this question we have to add two fractions for that we have to make denominator same this can be done by taking LCM. LCM is the least common multiple of two integers. We will use the prime factorization method to find the LCM. In prime factorization method the simply put the factor of each number and then for LCM we take product of factors, but we consider the repeated factors only one time but with highest exponent.

The correct answer is: $19 over 22$

Step1: First we will write all the prime factors of the denominators
In this question the denominators are $11$ and $22$ .
Factors of $11$ are: $11 to the power of 1$
Factors of $22$ are: $2 to the power of 1 cross times 11 to the power of 1$
Step2: For calculating the LCM we will multiply the factors by considering the common factors only one time with the highest exponent.
In this case the factor $11$ is common in both $11$ and $22$ so we will multiply it only once with the highest exponent
LCM ( $11$ , $22$ ) = $2 to the power of 1 cross times 11 to the power of 1$
LCM ( $11$ , $22$ ) = $22$
Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then add them
So, $22 over 11 space equals space 2$
and $22 over 22 equals 1$
So, we will multiply the numerator of $11$ by and numerator of $22$ by .
$fraction numerator 9 cross times 1 plus 5 cross times 2 over denominator 22 end fraction space equals 19 over 22$
So, the sum of $9 over 22 space and space 5 over 11$ is $19 over 22$ .

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